Combinatorial models for heterogeneous system composition and analysis

Complex systems with high dimensional design spaces are often specified by subsystem compositions that constrain feasible designs towards tight regimes in the design space. Composition between (sub)systems is limited by the interfaces exposed by the interacting architectures. Treating architectures as first class objects with their own formal properties is required to enable designing complex systems by novel compositions of heterogeneous subsystems and their design spaces. We describe a combinatorial model for system architectures using the formalism of cellular sheaves to identify all feasible compositions across heterogeneous subsystems through exposed interfaces. We discuss how the proposed model may be used to automatically generate novel systems of systems compositions and test key properties of composability and compositionality, required for solving planning and reconfiguration problems in systems of systems design.